Ngati Tama tribal leaders lodged a land claim for the area, site of its village before the tribe was driven out by military force in the early 1840s.
Tribal members also lodged claims to other parts of Wellington, first conquered by their ancestors in the early 1820s.
"Not only was it stolen but our tribe has been ignored in the history of Wellington - the future of New Zealand is being built on lies," said Ngati Tama Te Kaeaea Trust chairman, Tuffy Whare Churton.
"The Beehive [Parliament's Cabinet office wing] is probably the most important building in the country - but it's on land that was stolen from our people."
The tribe said it did not necessarily want the return of all lands claimed, and was open to negotiations. "We're not going to dig our toes in and be unrealistic but we would like to be acknowledged," Mr Churton said, adding that the government needed to "get its own house in order" before it tried to lead the nation. He warned that Parliament could be cursed with bad luck until the government had resolved the issue.
Ngati Tama was one of several indigenous Maori tribes that journeyed south from Taranaki and conquered the region early last century.
The tribe lived undisturbed from around 1824 until the early 1840s, when its chief was imprisoned by British colonisers and its people driven north.
Mr Churton said his ancestors were forced off their lands around 1843. Most retreated back to their Taranaki allies, several hundred miles to the northwest. He and other descendants of Ngati Tama chief Taringakuri told Waitangi land claim tribunal members that Ngati Tama had refused to sell its lands to white settlers, and was driven out of the city.
Doug Graham, the Treaty Negotiations Minister, declined to comment on the claim.